muavr-laplasning lokal va integral teoremalari

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1576482346.doc ¥ ® n ) ( m p n npq np m x x p n m m - = = , , 2 2 2 1 ) ( x e x p j = n a p 1 0 x 5 , 0 ) ( » x ф ) ( x ф ) , ( 2 1 m m p n ) ( ) ( ) ( ) , ( 2 1 a ф b ф dx x m m p b a n - = = ò j 005 , 0 = p 10000 = n 0 1 = m 70 2 = m 005 , 0 = p 995 , 0 = q 053 , 7 = npq npq np m a - = 1 089 , 7 - = a npq np m b - = 2 836 , 2 = b du e x x …

(6). belgilash kiritamiz: deb belgilaymiz. u holda (2) va (3) ga asosan: embed equation.3 . (7) yetarlicha katta bo`lganda va larni yetarlicha kichik qilish mumkin? shuning uchun va larni darajali qatorga yoyish mumkin. (8) (9) (8) va (9) larga asosan (7) ni quyidagicha yozish mumkin: embed equation.3 embed equation.3 bo`lgani uchun da (10) (2) va (3) larni hisobga olsak, , (11) va da (12) (6), (10), (11), (12) larni hisobga olsak (4) dan teoremaning isboti kelib chiqadi. masalalar yechishda qulaylik tug`dirish uchun funksiya uchun jadval tuzilgan. bu jadval faqat argumentning manfiy bo`lmagan qiymatlari uchun tuzilgan. juft bo`lgani uchun ning manfiy qiymatlari uchun ham shu jadvaldan foydalanish mumkin. masalalar yechiashda quyidagi taqribiy formuladan foydalaniladi: (13) endi oldingi ma`ruza oxirida keltirilgan masalani (13) formuladan foydalanib yechamiz. masala shartiga ko`ra: , , , . ; . demak, . muavr-laplasning lokal teoremasidan foydalanmasdan o`tkazilgan aniq hisolashlar ekanligini ko`rsatadi. taqribiy va aniq qiymat orasidagi farq …

anib maslalalar yechishda funksiyaning qiymatini hisoblashga to`g`ri keladi. funksiya qiymatlari uchun jadval tuzilgan. jadvalda funksiyaning nol va musbat larga mos qiymatlari keltirilgan. da funksiyaning toqligidan foydalanib, jadvaldan bo`lgan holda ham foydalanish mumkin. jadvalda ning kesmadagi qiymatlari berilgan, agar bo`lsa, u holda deb olinadi. funksiya orqali ni quyidagicha ifodalash mumkin: endi quyidagi masalani yechamiz: masala. korxonada ishlab chiqariladigan har bir maxsulotning yaroqsiz bo`lish ehtimoli . 10000 ta ishlab chiqarilgan maxsulot orasida yaroqsizlari soni 70 tadan oshmaslik ehtimolini toping. ; ; ; ; ; ; ; ; ; . funksiya jadvalidan ; . faraz qilaylik muavr-laplasning integral teoremasidagi barcha shartlar bajarilgan bo`lsin. biz nisbiy chastotaning o`zgarmas ehtimoldan chetlanishning absolyut qiymati bo`yicha oldindan berilgan sondan katta bo`lmaslik ehtimolini topish masalasini qaraymiz, ya`ni tengsizlikni bajarilish baholaymiz. muavr-laplas integral teoremasiga asosan shunday qilib (17) (17) ning ikkala tomonidan da limitga o`tsak, . . bu munosabatga bernulli sxemasi uchun katta sonlar qonuni yoki bernulli teoremasi deyiladi. …

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1576482346.doc ¥ ® n ) ( m p n npq np m x x p n m m - = = , , 2 2 2 1 ) ( x e x p j = n a p 1 0 x 5 , 0 ) ( » x ф ) ( x ф ) , ( 2 1 m m p n ) ( ) ( ) ( ) , ( 2 1 a ф b ф dx x m m p b a n - = = ò j 005 , 0 = p 10000 = n 0 1 = m 70 2 = m 005 , 0 = p 995 , 0 = q 053 , 7 = …

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